A U-shaped wire is placed before a concave having radius of curvature 20 cm as shown (18-E1). Find the total length of the image.

Answer

`116 cm`

Explanation

For `AB`
`(1)/(v)+(1)/(u)=(2)/(R)`
`(1)/(v_(1))=(2)/(-20)+(1)/(15)=-(1)/(10)+(1)/(15)=(-3+2)/(30)=-(1)/(30)`
`v_(1)=-30`
`m_(1)=-(v)/(u)=-((-30))/(-15)=-2`
For `CD`
`(1)/(v)=(1)/(-10)+(1)/(20)=(-2+1)/(20)=-(1)/(20)`
`v=-20`
`m_(2)=-(v)/(u)=-((-20))/(-20)=-1`
`m_(2)=-1`
Total `=2+10+4=16 cm`